In general , when gas accretes on to a supermassive black hole binary it is likely to have no prior knowledge of the binary angular momentum .
Therefore a circumbinary disc forms with a random inclination angle \theta to the binary .
It is known that for \theta < 90 ^ { \circ } the disc will coalign wrt the binary .
If \theta > 90 ^ { \circ } the disc wholly counteraligns if it satisfies \cos \theta < - J _ { d } / 2 J _ { b } , where J _ { d } and J _ { b } are the magnitudes of the disc and binary angular momentum vectors respectively .
If however \theta > 90 ^ { \circ } and this criterion is not satisfied the same disc may counteralign its inner regions and , on longer timescales , coalign its outer regions .
I show that for typical disc parameters , describing an accretion event on to a supermassive black hole binary , a misaligned circumbinary disc is likely to wholly co– or counter–align with the binary plane .
This is because the binary angular momentum dominates the disc angular momentum .
However with extreme parameters ( binary mass ratio M _ { 2 } / M _ { 1 } \ll 1 or binary eccentricity e \sim 1 ) the same disc may simultaneously co– and counter–align .
It is known that coplanar prograde circumbinary discs are stable .
I show that coplanar retrograde circumbinary discs are also stable .
A chaotic accretion event on to an SMBH binary will therefore result in a coplanar circumbinary disc that is either prograde or retrograde with respect to the binary plane .